This invention pertains generally to catoptric lens arrangements and particularly to arrangements of such sort used to direct wave-propagated energy.
For convenience, the following definitions will be used in connection with the catoptric lens arrangements referred to hereinafter.
A. FOCAL CURVE -- THE LOCUS OF THE FOCAL POINT OF A GENERATRIX OF A REFLECTING SURFACE WHEN SUCH GENERATRIX IS MOVED RELATIVE TO A REFERENCE LINE; IF THE GENERATRIX IS ROTATED, OR NUTATED, ABOUT AN AXIS OF SYMMETRY NOT PASSING THROUGH THE FOCAL POINT, THE FOCAL CURVE MAY BE REFERRED TO AS A FOCAL CIRCLE OR FOCAL ARC; IF THE GENERATRIX IS TRANSLATED WITH RESPECT TO ITS AXIS OF SYMMETRY, THE FOCAL CIRCLE MAY BE REFERRED TO AS A FOCAL LINE;
B. MERIDIONAL PLANE -- ANY CROSS-SECTIONAL PLANE PASSED THROUGH NONPARALLEL REFLECTING SURFACES HAVING A COMMON AXIS OF SYMMETRY IN A MANNER THAT SUCH COMMON AXIS AND THE NORMAL TO THE REFLECTING SURFACES AT ANY POINT ON THE LINES OF INTERSECTION BETWEEN THE CROSS-SECTIONAL PLANE AND NONPARALLEL REFLECTING SURFACES LIE IN THE CROSS-SECTIONAL PLANE; IF THE REFLECTING SURFACES THEMSELVES ARE DIVERGENT PLANES, ANY CROSS-SECTIONAL PLANE ORTHOGONAL TO BOTH REFLECTING SURFACES AND TO THE INTERSECTION BETWEEN SUCH SURFACES IS A MERIDIONAL PLANE;
C. NONMERIDIONAL PLANE -- ANY CROSS-SECTIONAL PLANE PASSED THROUGH NONPARALLEL REFLECTING SURFACES HAVING A COMMON AXIS OF SYMMETRY TO INTERSECT SUCH AXIS AT A POINT, ALL OF THE NORMALS TO THE REFLECTING SURFACES ALONG THE LINES OF INTERSECTION BETWEEN SUCH CROSS-SECTIONAL PLANE AND SUCH NONPARALLEL REFLECTING SURFACES NOT LYING IN SUCH PLANE;
D. REFLECTION PLANE -- ANY PLANE DEFINED BY A RAY INCIDENT ON A REFLECTING SURFACE AND THE NORMAL TO SUCH SURFACE AT THE POINT OF INCIDENCE; IF ANY PARTICULAR REFLECTION PLANE IS COINCIDENT WITH A MERIDIONAL PLANE, ALL RAYS IN THAT REFLECTION PLANE MAY BE REFERRED TO AS MERIDIONAL RAYS AND IF ANY PARTICULAR REFLECTION PLANE IS COINCIDENT WITH A NONMERIDIONAL PLANE, ALL RAYS IN THAT REFLECTION PLANE MAY BE REFERRED TO AS NONMERIDIONAL RAYS;
E. IDEAL RAY -- ANY RAY THAT ACTUALLY OR APPARENTLY ORIGINATES AT, OR IS (AFTER REFLECTION) DIRECTED TOWARD, A FOCAL POINT OR A FOCAL CURVE OF A REFLECTING SURFACE; IF THE GENERATRIX OF THE REFLECTING SURFACE IS A PARABOLA, SUCH A CURVE IS HEREINAFTER DEEMED TO HAVE AN IMAGINARY FOCAL POINT, OR FOCAL CURVE, AT INFINITY;
F. MERIDIONAL PLANE ABERRATION -- THE ANGULAR DIFFERENCE, IN ANY MERIDIONAL PLANE, BETWEEN AN IDEAL RAY REFLECTED FROM A POINT ON A REFLECTING SURFACE AND ANY MERIDIONAL RAY REFLECTED FROM THE SAME POINT;
G. NONMERIDIONAL PLANE ABERRATION -- THE ANGULAR DIFFERENCE, MEASURED IN ANY REFLECTION PLANE COINCIDENT WITH A NONMERIDIONAL PLANE, BETWEEN AN IDEAL RAY REFLECTED FROM A POINT ON A REFLECTING SURFACE AND ANY NONMERIDIONAL RAY IN THAT REFLECTION PLANE AND REFLECTED FROM THE SAME POINT;
H. Rambauske mirrors -- at least a pair of mirrors wherein the generatrices of the reflecting surfaces are sections of curves having a focal point moved relative to a reference line to cause the locus of each one of the focal points to be a focal curve as defined hereinbefore; in a catoptric lens arrangement, two, or more, Rambauske mirrors may be positioned so that their focal curves are coincident, i.e. confocal, or spaced one from another in a predetermined manner.
It is known in the art that a catoptric lens arrangement may be utilized to direct substantially coherent wave-propagated energy, as light in a beam from a laser, in any desired manner (within limits imposed by the effects of diffraction arising out of the finite dimensions of the exit aperture of such an arrangement). Thus, as described in detail in the copending U.S. application of Werner R. Rambauske, entitled "Catoptric Lens Arrangement," Ser. No. 244,393, filed Apr. 17, 1972, (which application is assigned to the same assignee as this application) various diffraction-limited catoptric lens arrangements are shown. The just-cited application shows that a catoptric lens arrangement incorporating at least two confocal Rambauske mirrors may direct a laser beam, or a beam of any type of wave-propagated energy. In particular, the cited application shows that the Rambauske confocal mirrors may have reflecting surfaces whose generatrices are portions of any quadratic conic sections (excepting the circle) rotated or nutated about axis of symmetry not containing both focal points of the selected curve. (As noted hereinbefore in the definition of an ideal ray, if the generatrix is a portion of a parabola, a virtual focal point at infinity may be deemed to be the second focal point). All rays in a beam from an ideal source of coherent wave-propagated energy positioned at one focal point of the entrance mirror in such an arrangement are, therefore, ideal rays which are directed without aberration by such an arrangement.
As noted, the catoptric lens arrangement shown in the cited application is used to direct the rays in a beam from a laser. While such a device may ordinarily be considered to be a completely coherent source, i.e. a point source producing a narrow beam, it is self-evident that a completely coherent source is a physical impossibility. That is, some of the rays from even a laser are not ideal rays. Further, it is obvious that the positioning of a laser so that its beam apparently originates at a focal point of any catoptric lens arrangement may be difficult to achieve. Mispositioning of the laser adds to the deviation of the rays in the beam from ideal.
Fortunately, when a laser is used as a source of coherent light, even the aberrations (if such are significant) caused by the just-mentioned anomalies may be substantially reduced by adjustment of any catoptric lens arrangement using Rambauske mirrors. That is, as described in the cited application, the relative positions of the Rambauske mirrors may be adjusted so that their focal curves are not coincident, but rather are spaced apart along the line between the coherent source and such mirrors. With proper spacing between such mirrors, at least "narrow field" aberrations, i.e. spherical aberration and coma, may be significantly reduced to attain diffraction-limited operation. This is so even though the source may be not perfectly coherent or positioned.
While the just-mentioned method of compensating for narrow field aberrations is effective when light from an almost completely coherent source, as a laser, is passed through any known catoptric lens arrangement using Rambauske mirrors, a different situation obtains when light from an extended source, as an incandescent or a fluorescent lamp, is to be formed into a beam. That is, because the rays from each different point in an extended source are spatially different, the compensation technique used for eliminating (for all practical purposes) aberrations resulting from inherent characteristics or positioning of any known coherent source may not lead to totally successful results when light from an extended source is to be corrected for aberrations.
When light from an extended source, as a luminescent filament in an incandescent lamp, is to be directed in a beam of any desired shape, it is well known to combine reflective and refractive lens elements to form such a beam. Thus, for example, conventional headlamps for automobiles usually incorporate the combination of a concave paraboloidal mirror and a refractive lens disposed over the exit aperture of such a mirror. An incandescent light is disposed as near the focal point of the concave paraboloidal mirror as possible. Light reflected from such mirror then is directed through the refractive lens, along with unreflected light from the incandescent light. Obviously, because the light finally passing through the refractive lens apparently originates at many different points, a simple refractive lens cannot properly direct all of such light. The refractive lens in a conventional headlamp, therefore, is made up of a number of lenslets, each covering a relatively small portion of the exit aperture of the concave paraboloidal mirror. With such design, each lenslet may be shaped and oriented so that the finally emergent light is directed generally in a desired direction.
Although an acceptable beam may be formed by a conventional automobile headlamp, many difficulties and shortcomings are experienced. For example, light falling on the junction between adjacent lenslets cannot be properly directed. Such light, if permitted a pass without change, contributes to glare in the eye of an observer; on the other hand, if redirected, such light contributes little, if any, illumination in the desired field. Further, because of the curvature of each lenslet, some of the light falling on the surface may be reflected back onto the paraboloidal mirror and, after further reflection, either contribute to glare or be lost. Finally, and probably most important from the point of view of the optical designer, the necessity of using many lenslets, each having its own axis of symmetry but required to redirect rays apparently originating at points on or off such axis, makes it manifest that the optimum design of each one of such lenslets may be, at best, a compromise design. That is, optimum design involves balancing the effects of incorrectible deficiencies, rather than increasing efficiency or providing a better beam.